You are to construct a decorative wood shelf that has two metal angle supports that fasten to the bottom of the shelf and resemble a right triangle. The shelves are to stick out from the wall 1 foot, and the diagonal distance of the metal piece is 1.25 feet. Using the inverse of sine, what is the approximate angle formed where the metal piece rests on the wall?(1 point)

Question

Responses

53°
53°

37°
37°

61°
61°

90°
90°

Answer 1

To find the angle formed where the metal piece rests on the wall, we can use the relationship involving the sine function in a right triangle.

We know:

• The opposite side (height from the wall to the bottom of the shelf) is 1 foot (1 ft).
• The hypotenuse (the diagonal distance of the metal piece) is 1.25 feet (1.25 ft).

The sine of the angle (\( \theta \)) formed with the wall can be expressed as follows:

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{1}{1.25} \]

Calculating this, we have:

\[ \sin(\theta) = \frac{1}{1.25} = 0.8 \]

Now, we calculate the angle \( \theta \) using the inverse sine function:

\[ \theta = \sin^{-1}(0.8) \]

Using a calculator:

\[ \theta \approx 53.13° \]

Rounding to the nearest degree, the angle is approximately:

\[ \theta \approx 53° \]

Therefore, the appropriate response is:

53°